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The problem asks:

Problem

I don't even know where to start. Do I need to find the width of the shaded areas, or something else completely?

UPDATE: Using the information given here, I was able to act as if the circles were inside of a square and use those methods.

Thank You

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marked as duplicate by user228113, RKD, GNUSupporter 8964民主女神 地下教會, Blue geometry Dec 10 '17 at 23:31

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  • $\begingroup$ Hint: draw some sectors, and find the area of the curvy bit. $\endgroup$ – Sean Roberson Dec 10 '17 at 23:10
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    $\begingroup$ see answers of this $\endgroup$ – achille hui Dec 10 '17 at 23:11
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    $\begingroup$ By symmetry, integrate in polar coordinates from $0$ to $\pi/4$, then multiply by 8. The polar equation of the uppermost circle is $r=a\sin\theta$ for a circle of radius $a$. $\endgroup$ – Alexander Burstein Dec 10 '17 at 23:15
  • $\begingroup$ @achillehui, Thank You, I didn't realize those methods would be applicable here. $\endgroup$ – The Math Guy Dec 10 '17 at 23:18

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